1. Field of the Invention
The present invention pertains to digital imaging systems. More particularly, this invention relates to a digital imaging system with an anti color aliasing filter.
2. Description of the Related Art
As is known, a digital imaging system typically includes an optical arrangement for imaging an object or objects of interest onto a sensor. The sensor has many discrete monocolor pixels that sample the image formed on the sensor by the optical arrangement. The sensor provides the digitized raw image. The digitized raw image is then manipulated by a digital image processing system of the digital imaging system to form the final image.
In order to achieve perfect image reconstruction in a digital imaging system, it is necessary for the sensor to sample the image captured by the imaging system at the Nyquist or higher rate. This means that each line pair or optical line of the image is sampled twice by the sensor pixels.
The overall resolving capability of a digital imaging system can be summarized in the form of its Modulation Transfer Function (MTF) which typically indicates the system's response to different spacial frequencies. The MTF is defined as the ratio R between the magnitude variation or modulation of the image intensity and that of the object. The ratio R can be expressed as follows:
R=(I.sub.max (image) -I.sub.min (image))/(I.sub.max (object) -I.sub.min (object)),
wherein I.sub.max (image) represents the maximum image intensity, I.sub.min (image) represents the minimum image intensity, I.sub.max (object) represents the maximum object intensity, and I.sub.min (object) represents the minimum object intensity.
In an ideal situation, the imaging optics provides a high modulation transfer of the frequencies at or below the sampling frequency (Nyquist) and, at the same time, a very small modulation transfer of the frequencies much higher than the sensor sampling rate.
FIG. 1 shows a representative behavior of three typical digital imaging systems in response to a range of spacial frequency input signals 11 through 13. As can be seen from FIG. 1, each digital imaging system has different MTF responses (i.e., 11a-11c, 12a-12c, and 13a-13c) at the three object frequencies 11-13. FIGS. 2A and 2B show the MTF plots of each of the three imaging systems with respect to a range of frequencies, along with a typical visibility line or a minimum detectable modulation level.
When the modulation of the image falls below the overall minimum detectable modulation level of the system which constitutes the minimum detectable modulation level of the sensor and the viewer's eye, the object pattern is considered not resolvable. Thus, the visibility line represents an upper limit for the resolving power of any practical imaging system. As can be seen from FIGS. 2A-2B, this upper resolution limit is the spacial frequency where the visibility line crosses the MTF curve for each specific system, giving a resolvable object area bounded by the visibility line and the MTF curve. Within this area, the MTF curve represents the visibility of the object at the specific frequencies.
When an imaged object contains some form of repeated patterns, the discrete form of sampling of the digital imaging system can inherently result in Moire pattern on the final image. The Moire pattern is caused by the interference between the image pattern frequency and the sampling frequency. This effect is typically referred to as image aliasing. A strong possibility of aliasing exists at the visible portion of the MTF curve, if the spacial sampling frequency of the detection system falls substantially below the resolving frequency limit of the imaging system. This area is marked as hatched area in FIG. 2B for the above systems. Curve 21 represents number 1 system, curve 22 represents number 2 system, and curve 23 represents number 3 system.
As can be seen from FIG. 2B, while the numbers 1 and 2 systems (represented by the curves 21 and 22) have a fairly large range of frequencies prone to aliasing, the number 3 system (represented by the curve 23) has an upper resolution or visibility limit close to the sampling frequency and therefore would not show any aliasing effect.
Complete characteristics of an imaging system can be represented by its unique MTF curves. Each independent MTF curve can represent the imaging capability of the system at any object location (relative to the axial point) at any wavelength. Since the various MTF curves are independent responses, the portions of the MTF curves that are prone to aliasing in each case may occur at different frequency range and present different modulation level. Thus, aliasing may not occur with the same strength or at the same frequency for all the image locations. In addition, it may show some color characteristics. This is due to the imaging system having different modulation levels for the different colors at any particular aliasing frequency. This effect is referred to as color aliasing.
In a typical optical imaging system, different colors present in the imaging operation are equally corrected. This means that the MTF of the typical optical imaging system is such that the chromatic MTF is closely coupled with the MTF of individual colors. In such a system, color aliasing could result from a color dependent sampling rate at the sensor array when the imaging system is a digital imaging system.
To achieve color sampling in digital imaging systems, a different color filter (referred to as color mosaic) is used in front of the individual pixel elements of the sensor. Since the distribution of these color mosaics could vary from one color to another, depending on the specific color imaging processing technique used, different colors may be sampled at different sampling rates. FIG. 3 shows a color mosaic of a typical digital imaging sensor array. FIGS. 4A-4C illustrate the sampling rates for green, red, and blue colors of the color mosaic pattern of FIG. 3. As can be seen from FIGS. 4A-4C, the sampling rate of the red and blue colors of the color mosaic pattern in FIG. 3 are different from that of the green color. This in turn means that the different colors may start to alias at different frequencies. In other words, a different lower frequency boundary is set for the aliasing prone area under the MTF curves of the different colors.
One prior solution to eliminating aliasing in general (not specifically color aliasing) is to customize the total resolving power of the optical system or to alter the overall (chromatic) MTF curve. To prevent color aliasing in specific, this alteration of the MTF has to be effective on the lowest sampled color of the imaging sensor.
The most common embodiment of this prior solution is to introduce a bi-axial birefringent crystal such as quartz, in the form of a filter, at close proximity to the imaging sensor. The double refraction function of the crystal, causes the image to be split into two separate images on the sensor. One image is formed by the undeviated ordinary rays and the second by the displaced extraordinary rays. The secondary image displacement is related to the filter thickness and is made such that it is equal to the sampling pitch of the sensor. Thus, image information with exact repeated pattern as the sampling pitch shows zero modulation in this case, and its information content is completely lost. This in effect could be thought of as a form of low pass filtering of the image information, whereby the MTF of the system for frequencies around and above the sensor pitch are severely altered for all wavelengths.
Alteration of the MTF in such a way that the modulation for all the frequencies beyond the sampling rate falls below the visibility limit, regardless of color, eliminates the possibility of having the digital imaging system extracting any high frequency information from the higher frequency sampled colors. This in effect is an overcorrection of the problem. A more proper way of taking care of the color aliasing problem would be to eliminate aliasing for the specific colors that show aliasing in lower frequencies independently and without affecting the higher frequency sample colors.